Question

the perimeter of a rectangular plot is 200 metres. its area is 2400 square metres . find length and breadth of rectangular plot​

Answer 1

Answer:

Step-by-step explanation:

We Have :-

Rectangular Plot having :-

Perimeter = 200 m

Area = 2400 m²

To Find :-

Length and Breadth of Rectangular Plot

Formula used :-

Perimeter of Rectangle = 2 ( Length + Breadth )

Area = Length * Breadth

Solution :-

Perimeter = 2 ( Length + Breadth )

200 = 2 ( l + b )

l + b = 100

l = 100 - b

Area = Length * Breadth

2400 = ( 100 - b ) * b

2400 = 100b - b²

0 = 100b - b² - 2400

b² - 100b + 2400 = 0

b² - 60b - 40b + 2400 = 0

b ( b - 60 ) - 40 ( b - 60 ) = 0

( b - 60 ) ( b - 40 ) = 0

So , b = 60 or b = 40

Case - 1

When

b = 60 m

l = 40 m

Case - 2

When

b = 40 m

l = 60 m

Answer 2

Answer:

case 1

Length $=$ 60 meter

Breadth $=$ 40 meter

case 2

length $=$40 meter

breadth $=$ 60meter

Step-by-step explanation:

Formula  perimeter of rectangle is 2$($L₊B$)$

2$($L₊B$)$ $=$ 200 meters

by dividing 2 both the side

L₊B $=$ 100 meters

L $=$ 100₋B $($ equation 1 $)$

Formula area of rectangle is L×B

L×B $=$ 2400 $meter^{2}$  $($ equation 2 $)$

by using equation 1st in equation 2st

$($100₋B$)$ ×B $=$2400

100B ₋ $B^{2} =$2400

$B^{2}$ ₋ 100B ₊ 2400 $=$ 0

$($ B ₋40 $) ($ B₋60$)$

B $=$ 40 meter

B $=$ 60 meter

by using formula area of rectangle

L×B $=$ 2400 $meter^{2}$  

case 1

L×40 $=$ 2400 $meters^{2}$

L $=$ 60 meter

case 2

L×60 $=$ 2400 $meters^{2}$

L $=$ 40 meter